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Examiner and lecturer

Hjalmar Rosengren

Literature

G. B. Folland: Fourier analysis and its applications, American Mathematical Society, 1992 (also published by Wadsworth & Brooks/Cole).
Folland's book will be sold by UBS during the first lecture September 3, 10.00. The price of the book is 600 SEK.

Further material

We will hand out some lecture notes.
Lecture notes 1 on Laplace transform.
Lecture notes 2 on Bessel's inequality.
Lecture notes 3 on the Gibbs phenomenon and periodic solutions to ODE.
Lecture notes 4 on inner product spaces.
Lecture notes 5 on filters.
Exercises.
Exercises for 15 October.
Corrections to Folland's book.
Some additional problems in Swedish and English. These exercises do not reflect the course content precisely.
Course content and theory check-list.
Questionnaire.

Preliminary programme

Normally, we will have lectures Monday 10-12 and Thursday 8-10, and exercise classes Monday 15-17 and Thursday 10-12.
My plan for the exercise classes is that the students should do most of the work. So if you want to participate I expect that you prepare at least a few of the suggested problems before the class.
F refers to Folland's book, N to lecture notes, E to the exercises that can be found above.

Day	Chapter	Content	Exercises
Th 3/9	N1, p. 1-9	Introduction, Laplace transform
M 7/9	N1, p. 10-14 F 1.3	More on Laplace transform Separation of variables	N1: 1,3,5,6,7,8,9
Th 10/9	F 2.1, N2	Fourier series: Introduction, Bessel's inequality	N1: 10,11,12,13,14,15
M 14/9	F 2.2-2.4	Fourier series: Proof of inversion theorem, further properties	F: 1.3.1, 1.3.7, Table 1: 2, 4, 6, 17 E: 1, 2, 3, 4
Th 17/9	F 2.5	Fourier series: Application to heat and wave equations	F 2.2.4, 2.4.3, 2.4.7, 2.4.11, 2.6.1 E 5, 6 7
M 21/9	N 3	Fourier series: Gibbs phenomenon, Periodic solutions of ODE	E 8, 9, 10, 11 F 2.5.1, 2.5.2, 2.5.7
Th 24/9	N4, F 3.1-3.4	Fourier series: L2 theory	E 10, 11, 13, 14 F 2.5.1, 2.5.2
M 28/9		Fourier series: L2 theory (continued) Sturm-Liouville problems (introduction)	E 15, 16, 17, 18, 20, 21 F 3.3.11
Th 1/10	F 3.5, 4.1-4.3	Sturm-Liouville problems Inhomogeneous boundary value problems	F 3.3.11, 3.5.2, 3.5.3, 3.5.5, 4.2.8
M 5/10	F 7.2	Fourier transform	F 3.5.1, 3.5.7, 4.2.2, 4.2.3, 4.2.4, 4.3.5, 4.3.6, 4.3.7
Th 8/10	F 7.2, 8.2 pp. 266-267	Fourier transform	E 22, 23, 24, 25 F 3.5.7, 4.3.7, 7.3.1
M 12/10	N5, F 7.3 pp. 229-231, 7.6 pp. 249-252	Fourier transform: Applications	E 26, 27, 28, 29, 30 F 7.2.12, 7.3.3
Th 15/10	F 4.4, 7.3 pp. 227-228	Harmonic functions Course evaluation	Exercises
M 19/10		Repetition

Examination

The exam will consist of 6 problems, giving a maximum of 24 points.
For MMG710 (GU students), grades are G (12-17 points) and VG (18-24 points).
For TMA362 (Chalmers students), grades are 3 (12-14 points), 4 (15-17 points) and 5 (18-24 points).
No calculator or handbook is allowed at the exam.
The exam takes place on 24 October, 8.30-13.30.

Tag med giltig legitimation och kvitto på erlagd kåravgift!
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Kontrollera att Du har fått rätt betyg och att poängsumman stämmer.
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Old exams

081025
090110
090819